Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 91 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Use a² − b² = (a + b)(a − b) to find 83² − 64².
2. 2.Use (a − b)² = a² − 2ab + b² to find 74².
3. 3.Use a² − b² = (a + b)(a − b) to find 40² − 37².
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 11.
6. 6.Use a² − b² = (a + b)(a − b) to find 79² − 72².
7. 7.Use (a + b)² = a² + 2ab + b² to find 23².
8. 8.Use (a + b)(a − b) = a² − b² to find 77 × 63.
9. 9.Use (a + b)(a − b) = a² − b² to find 107 × 93.
10. 10.Use (a − b)² = a² − 2ab + b² to find 53².
11. 11.Find the value of x² + 2xy + y² when x = 12 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 21² − 8².
13. 13.If a − b = 9 and ab = 10, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 76² − 4².
15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 26² − 4².
17. 17.Use (a + b)² = a² + 2ab + b² to find 36².
18. 18.Use a² − b² = (a + b)(a − b) to find 35² − 6².
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 11.
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 83².
22. 22.Use (a + b)² = a² + 2ab + b² to find 31².
23. 23.Use (a + b)² = a² + 2ab + b² to find 63².
24. 24.Find the value of x² + 2xy + y² when x = 12 and y = 2.
25. 25.Use (a + b)² = a² + 2ab + b² to find 26².
26. 26.Use (a − b)² = a² − 2ab + b² to find 28².
27. 27.Use (a + b)(a − b) = a² − b² to find 41 × 39.
28. 28.If a − b = 5 and ab = 6, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 57².
30. 30.If a + b = 9 and ab = 20, what is a² + b²?
31. 31.If a + b = 21 and ab = 108, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 54² − 4².
33. 33.Use (a + b)(a − b) = a² − b² to find 92 × 88.
34. 34.Use (a + b)(a − b) = a² − b² to find 57 × 43.
35. 35.If a + b = 10 and ab = 24, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 79 × 61.
37. 37.If a + b = 12 and ab = 20, what is a² + b²?
38. 38.If a − b = 2 and ab = 24, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 32².
40. 40.Find the value of x² − 2xy + y² when x = 10 and y = 8.

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